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 Post subject: Disjoint Groups DO Pairs
PostPosted: Thu Apr 09, 2015 12:27 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Disjoint Groups DO Pairs

The cages are ordered increasing top left to bottom right (row first).
The cages are digital - the last digit of the sum is in one of the cells.
The two cells are consecutive - the third one is non-consecutive so obviously NC C C or C C NC

Cages overlap in r1c1, r23c1, r4c4 r8c7 and r8c8.

Note it uses disjoint groups - I have done one of these for a few years.
Note it is X.

Quite hard, JS uses three fishes; please give your views on the hardness score.


Image

JS Code does not work with overlaps and disjoint groups, however I have attached the .jsd file as a zip.


(Moderator) In case the above diagram isn't clear enough, here are separate images for the cage patterns (by Ed) and background (by Andrew)
There are overlapping cages r1c1+r2c2+r3c3, r123c1 and r234c1 in n1
r4c4+r5c5+r6c6 and r456c4 in n5
r789c7, r7c89+r8c8 and r8c789 in n9
In the background, each colour such as cells r147c147 must contain 1-9.

Image Image

Solution:

261953487
384627591
759481623
826315749
913742856
547896312
692578134
435169278
178234965


Attachments:
DG X DO pairs.zip [2.55 KiB]
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PostPosted: Fri Apr 10, 2015 11:07 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for another interesting puzzle. Not difficult for anyone who has done previous puzzles with digitised, ordered CNC cages. The hardest part for me was keeping track of the disjoint groups, but I quickly got used to that.

Maybe JSudoku needed 3 fishes to solve the overlapping cages; humans can do that more easily.

Here is my walkthrough:
Cages are ordered increasing from top to bottom and left to right.
The cages are digital, the last digit of the sum is in one of the cells.
Two cells have consecutive values, with the other non-consecutive so either C C NC or NC C C
R1C1, R23C1, R4C4, R8C7 and R8C8 are each in two cages.

1. Each cage must contain the last digit of the cage sum, with the other two digits totalling 10, so cage sums must be in the range 11 to 19.

11 = [128]
12 = [129/237]
13 = [238/346]
14 = [347]
No possible permutations for 15, since [456] would have three consecutive values
16 = [367]
17 = [278/467]
18 = [189/378]
19 = [289]

[I've gone straight into analysis of the cages; if I'd done Prelims based on step 1, some of the steps may have been slightly shorter.]

2a. The two cages at R1C1 share the same cell and are in the same nonet so must contain five different values. Only possibilities are [237/289] and [346/378] -> R1C1 = {23}
2b. The same applies for the two cages at R4C4 -> R4C4 = {23}
2c. Naked pair {23} in R1C1 + R4C4, locked for D\ and orange disjoint group
2d. R123C1 overlaps with R234C1, only possibilities using the permutations in step 2a for R123C1 are R123C1 = [237/346], R234C1 = [378/467] -> R1234C1 = [2378/3467], 3,7 locked for C1, 3 also locked for N1
2e. R123C1 = [237/346] -> diagonal cage at R1C1 = [289/378], 8 locked for N1 and D\
2f. Diagonal cage at R4C4 = [346] (only remaining possibility because no 3,8 in R5C5 + R6C6), placed for D\ -> R4C4 = 3, R5C5 = 4, placed for D/, R6C6 = 6, placed for pale green disjoint group
2g. Diagonal cage at R4C4 = [346] -> R456C4 = [378] -> R5C4 = 7, placed for yellow disjoint group, R6C4 = 8, placed for D/ and grey disjoint group
2h. R1C1 = 2 -> R1234C1 = [2378], R2C1 = 3, placed for yellow disjoint group, R3C1 = 7, placed for grey disjoint group and R4C1 = 8, placed for orange disjoint group
2i. R123C1 = [237] -> diagonal cage at R1C1 = [289] -> R2C2 = 8, placed for pink disjoint group and R3C3 = 9, placed for D\ and pale green disjoint group

3. Only possible permutations for cage at R4C5 are [128/129] -> R4C5 = 1, placed for green disjoint group, R5C6 = 2, placed for blue disjoint group, R5C7 = {89}

4. Only possible permutations for R789C7 are [128/129/189] -> R7C7 = 1, placed for orange disjoint group, R8C7 = {28}, R9C7 = 9, placed for grey disjoint group, R5C7 = 8, R8C7 = 2, placed for yellow disjoint group
[Or the more elegant way is R8C7 is first cell of R8C789, cannot be 8 -> R8C7 = 2.]

5. Only possible permutation for cage at R7C8 is [347] -> R7C8 = 3, placed for green disjoint group, R7C9 = 4, placed for purple disjoint group, R8C8 = 7, placed for pink disjoint group, R9C9 = 5, placed for pale green disjoint group

6. R8C7 = 2, R8C8 = 7 -> R8C789 = [278] -> R8C9 = 8, R9C8 = 6, placed for pale orange disjoint group, R9C1 = 1, placed for D/ and grey disjoint group

7. R9C3 = 8 (hidden single in C3), placed for pale green disjoint group -> cage at R7C3 = [238] (because no 7 in R8C2) -> R7C3 = 2, placed for D/ and purple disjoint group, R8C2 = 3, placed for D/

8. R1C9 = 7 (hidden single on D/), placed for purple disjoint group, R3C7 = 6 (hidden single on D/)
8a. Naked pair {45} in R12C7, locked for C7 and N3 -> R2C8 = 9, placed for D/ and pink disjoint group, R1C8 = 8, placed for green disjoint group, R46C7 = [73], R2C9 = 1, placed for blue disjoint group, R3C8 = 2, placed for pale orange disjoint group, R3C9 = 3, placed for pale green disjoint group, R4C6 = 5, placed for purple disjoint group, R4C3 = 6, R1C3 = 1, R4C8 = 4, placed for green disjoint group, R4C9 = 9, placed for purple disjoint group

9. Naked pair {15} in R5C28, locked for R5 -> R5C1 = 9, placed for yellow disjoint group
9a. Naked pair {45} in R2C37, locked for R2 -> R2C6 = 7

and the rest is naked singles, without using the diagonals and disjoint groups.


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